Effluent from a cow breeding base was remediated via a catalytic ozonation process that used Mn–Fe–Ce/γ-Al2O3 as the catalyst, which was prepared by the impregnation roasting method. The catalyst was found to significantly influence the treatment effects for hydroxyl radical generation. HO• generation was qualitatively and quantitatively investigated using 5,5-dimethyl-1-pyrroline-n-oxide (DMPO) reagent, electron paramagnetic resonance (EPR), and coumarin fluorescence techniques, and scanning electron microscopy–energy-dispersive X-ray spectroscopy (SEM–EDX), Brunauer–Emmett–Teller (BET) method, X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) tests were performed to illustrate the structure and physical chemistry properties of the catalyst. The results showed that the modified Mn–Fe–Ce/γ-Al2O3 ternary catalyst has excellent catalytic performance and that the introduction of Mn, Fe, and Ce promotes the formation of abundant oxygen defects on the catalyst surface, which is assumed to be responsible for HO• generation. The conversion of Ce(III)/Ce(IV) and electron transfer/ejection due to the substitution of Ce(III)/Ce(IV) for Mn(II)/Fe(II)/Fe(III) were considered the fundamental intrinsic reasons underlying oxygen defect formation. In addition, the conditions for HO• quenching in the system were studied with the reaction time and catalyst dosage as parameters. The results supply a new technique for treatment of dairy farming wastewater and offer guidance for understanding the reaction mechanism of ternary supporting transition-metal catalysts.